OG详解-OG5 数学2 Q23

Choice D is correct. Two fractions can be added together when they have a common denominator. Since k>0, multiplying the second term in the given expression by k​k​ yields (42ak)kk​​ , which is equivalent to42ak²​k​. Therefore, the expression42ak​+42ak​ can be written as42ak​+42ak²k​​ , which is equivalent to 42a+42ak²k . Since each term in the numerator of this expression has a factor of 42a, the expression 42a+42ak²kcan be rewritten as 42a(1)+42a(k²)k , or 42a(1+k²)k,  which is equivalent to 42a(k²+1)k.
Choice A is incorrect. This expression is equivalent to 42ak​+42ak​​. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This expression is equivalent to 42ak​+42ak​.